find dy/dx.x = t2, y = 6 − 8t

Answer:

$705

Step-by-step explanation:

($3400)(0.075) = $255 commission earned

Total wage for that week = $450 + $255 = $705

note:  this answer assumes that $450 is the weekly basic wage, not daily

The Blu-ray movie will cost approximately $36.42 in 5 years with an inflation rate of 12% and continuous compounding.

To calculate the future cost of the Blu-ray movie in 5 years with an inflation rate of 12% and continuous compounding, we can use the formula for continuous compound interest:

A = P * e^(rt)

Where:

A = Future value

P = Present value

e = Euler's number (approximately 2.71828)

r = Annual interest rate (in decimal form)

t = Time period in years

In this case, the present value (P) is $19.99, the inflation rate (r) is 12% or 0.12, and the time period (t) is 5 years. Substituting these values into the formula, we get:

A = 19.99 * e^(0.12 * 5)

Calculating the exponent first:

0.12 * 5 = 0.6

Then:

e^0.6 ≈ 1.82212

Finally:

A = 19.99 * 1.82212 ≈ 36.42

Using the formula for continuous compound interest, we calculated that a Blu-ray movie that costs $19.99 today will cost approximately $36.42 in 5 years, assuming an inflation rate of 12% and continuous compounding.

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Answer:

\(t=14.7\)

Step-by-step explanation:

In the equation: \(t-9.25=5.45\) we need to get \(t\) by itself. To do that, we need to add \(9.25\) from one side to the other. We do this because on the side where \(t\) is, \(9.25\) is being subtracted and we have to do the opposite of that. So:

\(t-9.25=5.45\)

  \(+9.25\)     \(+9.25\)

In this case, we got \(t\) by itself. The new equation is:

\(t=14.7\)

Answer:

i could  be wrong but B

Step-by-step explanation:

I assume it's D

S shows a variable you need to find to find how many students are in Social Studies class.

Answer:

The answer is 53.25

Step-by-step explanation:

Before Tax Price: $50.00

Sale Tax: 6.50% or $3.25

After Tax Price: $53.25

Given:

The terms are \(-3a^2b^2,-\dfrac{5}{2}a^2b^2,4a^2b^2,\dfrac{2}{3}a^2b^2\).

To find:

The sum of given terms.

Solution:

Sum of given terms is

\(-3a^2b^2+(-\dfrac{5}{2}a^2b^2)+4a^2b^2+\dfrac{2}{3}a^2b^2\)

\(=-3a^2b^2-\dfrac{5}{2}a^2b^2+4a^2b^2+\dfrac{2}{3}a^2b^2\)

Taking out common factors, we get

\(=\left(-3-\dfrac{5}{2}+4+\dfrac{2}{3}\right)a^2b^2\)

\(=\left(\dfrac{-18-15+24+4}{6}\right)a^2b^2\)

\(=\left(\dfrac{-5}{6}\right)a^2b^2\)

\(=\dfrac{-5}{6}a^2b^2\)

Therefore, the sum of given terms is \(\dfrac{-5}{6}a^2b^2\).

Answer:

Her answer is incorrect. At first glance 30/29 is greater than 1. When you multiply 60 by something greater than 1, the answer is going to be greater than 60.

Step-by-step explanation:

60(30/29) = 1800/29 = 62.07

No, Laura's answer is incorrect.

Fractions are used to represent smaller pieces (or parts) of a whole.

Given that, Laura wants to work out 30/29 of 60. Her answer is 58.

We see, 58 is smaller than 60, therefore, her answer is incorrect.

30/29 is greater than 1.

When you multiply 60 by something greater than 1, the answer is going to be greater than 60.

60(30/29) = 1800/29 = 62.07

Hence, Laura's answer is wrong.

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Answer: To find the ratio of the dimensions of the actual room to that of the scale model, we can divide the dimensions of the actual room by the dimensions of the scale model.

The dimensions of the actual room are 15m by 9m by 12m, and the dimensions of the scale model are 5m by 3m by 4m.

Therefore, the ratio of the dimensions of the actual room to that of the scale model is:

length: 15m / 5m = 3 : 1

width: 9m / 3m = 3 : 1

height: 12m / 4m = 3 : 1

So, the ratio of the dimensions of the actual room to that of the scale model is 3:1 for all dimensions (length, width, and height)

The ratio of the dimensions of the scale model to that of the actual object is 1:16

so to find the length and width of the actual object, you can use this relation

length = scale model length * 16 = 2.416 = 38.4m

width = scale model width * 16 = 1.816 = 28.8m

So the length and width of the actual object are 38.4m and 28.8m respectively.

Step-by-step explanation:

Answer:

Step-by-step explanation:

So 20% of the science club students is 10.

I am trying to find 100% as this equals ALL the students on the science club trip.

20% = 10

100% / 20% = 5

This means I need to multiply both sides by 5 to get to 100%
20% = 10

(Multiply both sides by 5)

100% = 50

Therefore there are 50 students in the science club (C)

The average rate of change of g(x)=x^2 on the interval 3≤x≤9 is 12

In this question, we have been given a function g(x)=x^2

We need to find the average rate of change of function on the interval 3 ≤ x ≤ 9

For x = 3,

g(3) = 3^2

g(3) = 9

and for x = 9,

g(9) = 9^2

g(9) = 81

So, the average rate of change would be,

g(9) - g(3) / [9 - 3]

= (81 - 9) / 6

= 72/6

= 12

Therefore, the average rate of change of g(x)=x^2 on the interval 3≤x≤9 is 12

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To estimate the mean EPA combined city and highway mileage, the automaker conducted EPA mileage tests on a random sample of 35 midsize cars. The sample mean is 24, and the population standard deviation is 1.2. The task is to calculate the 70% confidence interval for the population mean.

To calculate the confidence interval, we can use the formula:

Confidence Interval = Sample Mean ± (Critical Value) * (Standard Deviation / √(Sample Size))

First, we need to determine the critical value associated with a 70% confidence level. The critical value can be found using a standard normal distribution or a t-distribution, depending on the sample size and whether the population standard deviation is known.

Since the sample size is relatively large (n = 35), we can use the standard normal distribution. The critical value for a 70% confidence level corresponds to a z-score of ±1.036.

Next, we calculate the margin of error:

Margin of Error = (Critical Value) * (Standard Deviation / √(Sample Size)) = 1.036 * (1.2 / √35) ≈ 0.380

Finally, we can calculate the lower and upper bounds of the confidence interval:

Lower Bound = Sample Mean - Margin of Error = 24 - 0.380 ≈ 23.62

Upper Bound = Sample Mean + Margin of Error = 24 + 0.380 ≈ 24.38

Therefore, the 70% confidence interval for the mean EPA combined city and highway mileage is approximately 23.62 to 24.38.

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- 4 ( 7a + 7 ) - 2a = 92

- 28a - 28 - 2a = 92

- 28a - 2a - 28 = 92

Collect like terms

- 30a - 28 = 92

Add both sides 28

- 30a - 28 + 28 = 92 + 28

- 30a = 120

Divide both sides by - 30

- 30a ÷ - 30 = 120 ÷ - 30

Answer:

6

Step-by-step explanation:

In the slope- intercept form (y= mx +c), the slope is the coefficient of x.

Let's rewrite the given equation into the slope- intercept form.

6x -y= 1

6x= y +1

y +1= 6x

y= 6x -1

Since the coefficient of x is 6, the slope of the given line is 6. Parallel lines have the same slope and thus the slope of the line parallel to the given line is also 6.

The simplified form of the given expression is, 1/4d + f.

What is simplified form of the expression?

To simplify an expression, create an equivalent expression without any terms that are similar.

The expression will then be rewritten using the fewest terms possible.

Mathematical operations can be made much simpler by using the right order of operations. Exponents, terms in parentheses, multiplication, division, addition, and finally subtraction are the correct order of operations.

Consider the given expression,

1/2d - 3/4d + 3f - 2f

Here the like terms are '1/2d  and 3/4d' and '3f and 2f'.

To simplify the expression,

1/4d  + f

Hence, the simplified form of the given expression is, 1/4d + f.

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The percentage of tires that will have a life of 45,000 to 55,000 miles is  68.27%. So the correct option is 68.27%.

To find the percentage of tires that will have a life of 45,000 to 55,000 miles, we can use the concept of the normal distribution.

First, we calculate the z-scores for both values using the formula:
z = (x - mean) / standard deviation

For 45,000 miles:
z1 = (45,000 - 50,000) / 5,000 = -1

For 55,000 miles:
z2 = (55,000 - 50,000) / 5,000 = 1

Next, we look up the corresponding values in the standard normal distribution table. The table will provide the proportion of data within a certain range of z-scores.

The percentage of tires with a life between 45,000 and 55,000 miles is the difference between the cumulative probabilities for z2 and z1.

Looking at the standard normal distribution table, the cumulative probability for z = -1 is 0.1587, and the cumulative probability for z = 1 is 0.8413.

Therefore, the percentage of tires that will have a life of 45,000 to 55,000 miles is:
0.8413 - 0.1587 = 0.6826

Converting this to a percentage, we get:
0.6826 * 100 = 68.26%

So the correct answer is 68.27%.

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The height of the tower is approximately 336.4 feet. To find the height of the tower, we can use trigonometric ratios in a right triangle formed by the tower, the person's line of sight, and the ground.

Let's label the height of the tower as "h" in feet. We can divide the right triangle into two smaller triangles: one with the angle of elevation of 42 degrees and the other with the angle of depression of 28 degrees.

In the triangle with the angle of elevation, the side opposite the angle of elevation is the height of the tower, h, and the side adjacent to the angle of elevation is the distance from the window to the tower, which is 350 feet. We can use the tangent function to relate the angle of elevation and the sides of the triangle:

tan(42 degrees) = h / 350

Similarly, in the triangle with the angle of depression, the side opposite the angle of depression is also the height of the tower, h, and the side adjacent to the angle of depression is the distance from the window to the tower, which is still 350 feet. Using the tangent function again, we have:

tan(28 degrees) = h / 350

We can solve these two equations simultaneously to find the value of h. Rearranging the equations:

h = 350 * tan(42 degrees)

h = 350 * tan(28 degrees)

Evaluating these expressions, we find that h is approximately 336.4 feet.

Therefore, the height of the tower is approximately 336.4 feet.

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The power series expansion of 67 - x with centre c = 0 is: 67 - x = ∑n=0∞ (11 - 0ⁿ)(x - 0)ⁿ = ∑n=0∞ 11xⁿ.

Using the equation:

For |x| 1, 11 x = n=0 xn

In a power series with centre c = 0, we want to expand 67 - x using this expression.

To accomplish this, 67 - x must be rewritten as a function of (x - c), where c = 0:

67 - x = 67 - (x - 0) = 67 - (x - c) (x - c)

In the solution above, we can now change x to (x - c):

For |x - c| 1, the expression 11 - (x - c) = n=0 (x - c)n

for |x - c| 1, = 11 - n=0 (x - c)n

For |x - c| 1, = n=0 (11 - cn)(x - c)n

The power series growth of 67 - x with centre c = 0 is as follows:

67 - x = ∑n=0∞ (11 - 0ⁿ)(x - 0) (x - 0)

ⁿ = ∑n=0∞ 11xⁿ.

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Answer: 1/2

Step-by-step explanation:  I believe the answer is 1/2 because for (2,-6) and (4,-7) the rise over run is 1/2. I don't know though

Answer:

I think its C.

Step-by-step explanation:

Answer:

(-1, -4)

Step-by-step explanation:

Make the y value the opposite value.

Answer:

6t^13-12t^12

Step-by-step explanation:

6t^12(t-2)

6t^12t+6t^12*-2

6t^12+1 +6t^12*-2

6t^13+6t^12*-2

6t^13-12t^12

Answer:

how many weeks tho

Step-by-step explanation:

you don't make it clear sorry

Nina pay in property taxes 501. or \(5.01*10^{2}\).

A property tax, often known as a millage rate, is an ad valorem tax based on a property's value. The tax is imposed by the administrative body of the region where the property is situated. This could be the federal government, a federated state, a county, a region of land, or a municipality. The average effective property tax rate in the Lone Star State is 1.60%, making Texas' property taxes the seventh-highest in the nation. Comparing that to the current 0.99% national average will help. Property taxes in Texas cost the average homeowner $3,797 a year. It is well known that British property owners do not pay property tax. But hold on, it's too soon to celebrate because there might still be taxes to pay.

Based on the given conditions, formulate:

3340*15%

Calculate.

501

Alternative forms.

\(5.01*10^{2}\)

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Answer:

5c + 2

Step-by-step explanation:

you first of all group like terms together

2c + 3c + 6 -4

5c + 2

Answer:

y=17x-55

Step-by-step explanation:

y-(-4)=17(x-3)

y+4=17x-51

y=17x-55

Answer:

\(thank \: you\)

6n 1/2 y 1/2

its solved, here ypu go

The number of simple events in this experiment is 16.

The correct answer to the given question is option c.

The probability of an event can be calculated by dividing the number of favorable outcomes by the number of possible outcomes. A simple event is one in which only one of the outcomes can occur. For example, if a coin is tossed, a simple event would be the outcome of the coin being heads or tails.

The total number of possible outcomes in the experiment of tossing 4 unbiased coins simultaneously is 2⁴, since there are two possible outcomes for each coin. Thus, the total number of possible outcomes is 16.

Each coin has two possible outcomes: heads or tails. If all four coins are flipped, there are two possible outcomes for the first coin, two possible outcomes for the second coin, two possible outcomes for the third coin, and two possible outcomes for the fourth coin. Therefore, the total number of possible outcomes is 2 × 2 × 2 × 2 = 16.

Therefore, the number of simple events in this experiment is 16, which is option (c).

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To find the G.S. (General Solution) of the differential equation X" - 3x² - 4x = 15 Exp(4t) + 5 Exp(-T), we can use two different methods: Method 1 - using the characteristic equation and Method 2 - using the method of undetermined coefficients.

Method 1: The characteristic equation is r² - 3r - 4 = 0, which has roots r = -1 and r = 4. Therefore, the homogeneous solution is Xh(t) = C1 Exp(-t) + C2 Exp(4t). To find the particular solution, we assume Xp(t) = A Exp(4t) + B Exp(-t) and substitute it into the differential equation. Solving for A and B, we get Xp(t) = (3/5) Exp(4t) - (2/5) Exp(-t). Therefore, the general solution is X(t) = Xh(t) + Xp(t) = C1 Exp(-t) + C2 Exp(4t) + (3/5) Exp(4t) - (2/5) Exp(-t).
Method 2: We assume that X(t) = A Exp(4t) + B Exp(-t) + C is the particular solution. Substituting it into the differential equation, we get A(16) Exp(4t) - 3(B² Exp(-2t) + 2AB) Exp(4t) - 4(A Exp(4t) + B Exp(-t) + C) = 15 Exp(4t) + 5 Exp(-t). Equating the coefficients of the exponential terms, we get A(16) - 4A = 15 and -3B² + 8AB - 4B = 5. Solving for A and B, we get A = 3/5 and B = -2/5. Therefore, the particular solution is Xp(t) = (3/5) Exp(4t) - (2/5) Exp(-t) and the general solution is X(t) = Xh(t) + Xp(t) = C1 Exp(-t) + C2 Exp(4t) + (3/5) Exp(4t) - (2/5) Exp(-t).
In conclusion, the G.S. of the given DE is X(t) = C1 Exp(-t) + C2 Exp(4t) + (3/5) Exp(4t) - (2/5) Exp(-t).

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